= Solution
Eighteenth-century support for the Newtonian system accumulated through successful predictions, the resolution of apparent discrepancies and increasingly precise terrestrial tests. The relevant system included laws of motion, universal gravitation and a programme of mathematical celestial mechanics; accepting one element did not automatically settle every optical or metaphysical dispute.
<Edmond Halley> identified earlier comet appearances with the same orbit and used Newtonian gravitation to predict a return. Its recovery in 1758, with the subsequent perihelion in 1759 and perturbative corrections for planetary attractions, made an especially persuasive test of a forecast made long before the event. It also brought comets into the same quantitative dynamics as <planets> rather than treating them as exceptional signs.<Halley's comet history by NASA>[1705 prediction and eighteenth-century return]{ref}
Geodetic expeditions compared meridian arcs at different latitudes. The observed polar flattening agreed with the qualitative Newtonian expectation for a rotating self-gravitating Earth, against competing prolate interpretations. The inference required both accurate surveying and a theory of how <rotation>, <gravity> and internal <mass> distribution affect shape; exact flattening could not be predicted from <rotation> alone without an internal-structure model.<The figure of the Earth expedition by Académie des sciences>[Lapland expedition and oblate-Earth conclusion]{ref}
Lunar and planetary perturbation theory provided a sustained, more demanding test than unperturbed Keplerian <ellipses>. Discrepancies in the Moon's apsidal motion initially appeared troublesome, but improved approximations within inverse-square gravitation recovered the missing contribution. Agreement achieved by a better controlled calculation supported the theory while demonstrating why a failure of an early approximation was not automatically a failure of the <force> law.
<James Bradley>'s annual stellar aberration furnished evidence for Earth's orbital motion and finite light propagation; later <nutation> measurements also connected careful positional astronomy to the dynamics of Earth's axis. Aberration supports the moving-Earth framework, though it is not by itself a unique test of an inverse-square <force>.<Letter from James Bradley to Edmond Halley>[annual observations and mathematical analysis of stellar motion]{ref}
Finally, <Henry Cavendish>'s torsion-balance experiment in 1798 measured attraction between laboratory <masses> and inferred Earth's mean <density>. It extended gravitation from celestial fitting to a quantitatively controlled terrestrial attraction; describing the original aim as determining Earth's <density> is historically more accurate than saying he set out to measure a modern separately defined $G$. Together these tests supplied converging support across scales. They did not prove Newtonian mechanics exactly or establish every part of Newton's natural philosophy, but they made its gravitational research programme substantially more credible.
Back to article page
